Love Emotions between Laura and Petrarch � an Approach by Mathematics and System Dynamics

Abstract

Laura, a very beautiful but also mysterious lady, inspired the famous poet Petrarch for poems, which express ecstatic love as well as deep despair. F. J. Jones-a scientist for literary work-recognized in these changes between love and despair an oscillating behaviour-from 1328 to 1350-which he called Petrarch's emotional cycle. The mathematician S. Rinaldi investigated this cycle and established a mathematical model based on ordinary differential equation: two coupled nonlinear ODEs, reflecting Laura's and Petrarch's emotions for each other, drive an inspiration variable, which coincides with Petrarch's emotional cycle. These ODEs were the starting point for the investigations in two directions: mapping the mathematical model to a suitable modelling concept, and trying to extend the model for love dynamics in modern times (F. Breitenecker et al.). This contribution introduces and investigates a modelling approach for love dynamics and inspiration by means of System Dynamics, for Laura's and Petrarch's emotions as well as for a modern couple in love. In principle, emotions and inspiration emerge from a source and are fading into a sink. But the controlling parameters for increase and decrease of emotion create a broad variety of emotional behaviour and of degree of inspiration, because of the nonlinearities. Experiments including an implementation of this model approach and selected simulations provide interesting case studies for different kinds of love dynamics-attraction, rejection and neglect-stable equilibria and chaotic cycles.

Emotions as dynamic systems in viability sets

“…His modelling, whatever its efficacy, deals with the specific case of Laura and Petrarch and is not an attempt to characterize the very definitions of emotions, as is the present one. Breitenecker et al [24] extended this model of love to a 'man-woman' dynamic, producing stable equilibria and chaotic cycles. Their model also relies on conjectures about possible interactions between the actors.…”

Chaotic Dynamics of the Fractional-Love Model with an External Environment

“…Strogatz [ 22 ] and Sprott [ 21 ] explained the behavior of linear and nonlinear systems with respect to the love model, and also proposed the love model based on Shakespeare’s Romeo and Juliet . Actually, in mathematics, the love model is based on Romeo and Juliet and can be also defined as the Laura and Petrarch model [ 24 , 25 ] and the Adam and Eve model [ 26 ]. However, the “Romeo and Juliet” model is commonly used in the study of nonlinear dynamics by researchers.…”

Periodic Doubling and Chaotic Attractor in the Love Model with a Fourier Series Function as External Force

“…Love model have proposed several models including the Romeo and Juliet model [9][10][11][12][13], the Laura and Petrarch model [14,15], the Adam and Eve model [16], and others [17][18][19][20][21].…”